Studies on chaotic quantum systems

Bandyopadhyay, J. N.

As a model of decohering environment, we show that a quantum chaotic system behaves equivalently as a many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic environment is derived. This theoretical formulation is substantiated by the numerical study of the decoherence of two qubits interacting with a quantum chaotic environment modeled by a chaotic kicked top. Like the many-body model of environment, the quantum chaotic system is an efficient decoherer, and it can generate entanglement between the two qubits which have no direct interaction.

Boris V. Chirikov

Casati, Giulio

Jayendra N. Bandyopadhyay

As a model of decohering environment, we show that a quantum chaotic system behaves equivalently as a many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic environment is derived. This theoretical formulation is substantiated by the numerical study of the decoherence of two qubits interacting with a quantum chaotic environment modeled by a chaotic kicked top. Like the many-body model of environment, the quantum chaotic system is an efficient decoherer, and it can generate entanglement between the two qubits which have no direct interaction.

Rubens Viana Ramos, Rui Fragassi Souza

Quantum cryptography is a potential technique for data security in communications networks. However, it still must overcome some implementation problems to become commercial, such as the limited distance between network's users, low transmission rate of quantum data and the decoherence suffered by the quantum state during propagation in the channel. On the other hand, chaotic systems show rich dynamics with very interesting properties that can be used in communications. In this direction, we propose the use of suitable properties of chaotic systems, such as great sensitivity to initial conditions, unpredictability, controllability and synchronisation of chaotic systems to overcome some problems of quantum cryptography.

Jian‐Min Yuan, D.H. Feng, George M. Zaslavsky